1. Technical Field
The present disclosure relates to a method and apparatus for inversion processing of well logging data. More particularly, the present disclosure relates to a method and apparatus for deriving information regarding a subsurface geophysical formation through inversion processing of well logging data, acquired for the subsurface geophysical formation, in a selected pattern space. The present disclosure further relates to a method and apparatus for deriving information regarding a subsurface geophysical formation by combining information obtained during inversion processing of well logging data, acquired for the subsurface geophysical formation, in measurement space with information obtained during inversion processing of the well logging data in a selected pattern space.
2. Description of Related Art
Generally, inversion processing relates to a methodology by which model parameters are derived from measurement data. The inversion methodology involves a search for a minimum point of an object function, commonly referenced in the art as a misfit object function, which relates a set of field measurements acquired by a data acquisition device to a simulated response, commonly referenced in the art as a set of numerically forward-computed measurements, (or “model”) of the field measurements. When the misfit object function reaches its minimum point, the model used to determine the set of numerically forward-computed measurements is selected as the model underlying the field measurements. Typically, to search for the minimum point of the misfit object function, an iterative optimization scheme, which automatically adjusts the model parameters used to determine the numerically forward-computed measurements based upon the minimum point identified for prior computations of the misfit object function, is used.
The application of inversion processing techniques to well logging data was first disclosed in Lin et al., “Inversion of Induction Logging Data Using the Least Squares Approach”, 25th Annual Logging Symposium Transactions, pgs. AA1-AA14 (Society of Professional Well Log Analysts, 1984). While a variety of applications of inversion processing techniques to well logging data have since been disclosed, most such applications have focused on improving the stability of the inversion process using various regularizations and constraints. See, for example, Dyos, “Inversion of Induction Log Data by Method of Maximum Entropy”, 28th Annual Logging Symposium, pgs. T1-13 (Society of Professional Well Log Analysts, 1987) and Freedman et al., “Maximum Entropy Inversion of Induction Log Data”, Formation Evaluation, pgs. 259-268 (Society of Petroleum Engineers, 1991). The construction of the misfit object function has also been studied. For example, in Zhang et al., “Determining Bed Boundaries from Inversion of EM Logging Data Using General Measures of Model Structure and Data Misfit”, Geophysics, Vol. 65, pgs. 76-82 (Society of Exploration Geophysicists, January 2000), a 1-D nonlinear inversion of electromagnetic (“EM”) logging data utilizing a generic model object function was disclosed. However, like other implementations, the object function disclosed in Zhang et al. was bound to the misfit between the field measurements and the numerically forward-computed measurements.
Current inversion processes have yet to satisfactorily address the problems of poor resolution and simultaneity. More specifically, conventional inversion processes are implemented by minimizing the misfit between the field measurements and the numerically forward-computed measurements. Although some of the parameters to be inverted in a specific application relate to the measurements directly, others are only indirectly related to the measurements. The existence of these indirect parameters complicates the inversion process considerably. Since indirect parameters have, at best, only a very weak dependence to the misfit object function, they cannot be derived without large uncertainty and are, therefore, considered to be poorly resolvable. Additionally, as previously set forth, inversion processes typically include the use of iterative optimization schemes to derive the parameters. Oftentimes, however, parameters, including both direct and indirect parameters, must be solved simultaneously. In such situations, the efficiency and reliability of the inversion process is adversely affected.
While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.